Question

3. A train travels from Agra to Delhi with
a constant speed of 50 km h- and returns
from Delhi to Agra with a constant speed
of 40 km h-!. Find the average speed of
the train.
the ans = 44.4 km h‐¹
i want the formula explanation ​.

Answer 1

Given:-

→Speed of the train in it's first journey

from Delhi to Agra=50km/h

→Speed of the train in it's return journey

from Agra to Delhi=40km/h

To find:-

→Average speed of the train

Solution:-

Let the two speeds of the train be v₁ and v₂ respectively.

In this case,we can see that the distance travelled by the train in both the cases is same.

So,when distance travelled by a body is same in both cases,then average speed:-

=>Vₐᵥ = 2v₁v₂/v₁+v₂

=>Vₐᵥ = 2×50×40/50+40

=>Vₐᵥ = 4000/90

=>Vₐᵥ = 44.44km/h

Thus,average speed of the train is

44.44km/h.

Note: The above used formula can be used to find average speed/velocity of a body,only when it covers same distance in both cases.

Answer 2

44.4 km h

Explanation:

suppose the distance distance between agra and delhi is D Km

from relaton V = D / T , time taken = D / V

in the first part of the journey from agra to delhi, V1 = 50 km h

Time taken = D/VI - D km / 50 km h = (D/50) h

in second part of journey from delhi to agra speed v2 = D/V2 = D km/40 km h

total distance = D+D=2D

D/50 + D/40 = 9D / 200

average speed = Total distance/total time

2 D / (9D/200) hours

2x200 / 9 = 44.4 km h